Question

Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -1. Help please.

Answer 1

I have -2t=-7+3s & 1+2t=5s & 3t=1+5s. Where do I go from here?

Answer 2

If I isolate each variable, I get that t = 7/2 and s = 19/10, I am lost after that. I don't know what to do. Help please.

Answer 3

hey

Answer 4

did you try replace putting x+y-z=-1 in terms of t

Answer 5

\[x+y-z=-1 \\ (1+t)+(2t)-(-3t)=-1\]
Solve this for t

Answer 6

then you can find (x,y,z) the point of intersection

Answer 7

(x,y,z)=(1+t,2t,-3t)

Answer 8

Are you here?

Answer 9

yes I am

Answer 10

so you are saying that the result would be (0, -2, 3). Is that right?

Answer 11

what did you get for t?

Answer 12

-1/3 = t

Answer 13

ok isn't 1+(-1/3)=2/3

Answer 14

that would be the x-coordinate

Answer 15

and y=2t=2(-1/3)=-2/3
and z=-3t

Answer 16

so z=?

Answer 17

1

Answer 18

yep

Answer 19

okay I got it now. Thank you very much.

Answer 20

np